Four-point conductance measurements of a high temperature annealed monolayer of Pb on Si(557) are combined with tunneling microscopy (STM) and LEED for structural investigations. We found extremely high surface state conductance which becomes quasi-one-dimensional below a critical temperature of T c =78K. The change from low to extremely high conductance anisotropy is associated with a reversible order–disorder phase transition with a temperature dependence ∝1/T+const. along the chains below the phase transition. Below the phase transition order is found simultaneously in the lateral separation between Pb chains and along the chains. There a 10-fold superperiodicity appears. We suggest that strong two-dimensional coupling, leading to electronic stabilization of terraces with a width of 423 lattice constants, results in perfect nesting normal to the chains at E F (below T c ), which is the origin of this switching to one-dimensional behavior. Therefore, no metal–insulator transition is expected at low temperature.